"What is the most broken game that you tried and were unable to play?"
Oh Dungeons & Dragons...how amusing that you're here, and today, and I'm smiling.
I suppose I should qualify this by saying that it was one game of D&D that I found too broken to play, and the reason behind its brokenness had nothing to do with the system's mechanics.
It more or less had to do with the idiotic way the GM tried to implement every D&D system in existence for a new gaming store demo. And such was my introduction to Santa Fe's only gaming store. It's also one of the reasons I've never gone back.
Things began with my early arrival, eagerly awaiting CharGen. I'd signed up on their Facebook page to play, but noted that they hadn't provided a system for their game of D&D. Therefore, I took the liberty of printing out 3.5, 4.0, and Pathfinder character sheets. You know, just in case. Imagine my befuddlement upon appearing and being told that the game was being run for all systems of D&D.
Note that this statement is utterly different than saying that the system didn't matter for the game being run.
The resultant party consisted of a 4e rogue, a Pathfinder monk, and I think a 2e fighter? I must have blocked out most of the game, or simply no longer remember, because I left the table after a half hour trying to reconcile the varying types of skill challenges each player was using against the next. There was no plot. There was a tavern, I think. And an arrest.
And the rogue was a dickbag, which is actually pretty standard for a prepubescent playing a rogue.
So yeah, utterly broken game...fucking Realm.